Impact of fuzziness in measurement scale on basic statistical inference

Abstract

When a product, performance or service is rated or a behavioural response is sought, the alternatives typically do not have well-dened and universally understood demarcations. In this research, we address validity or inaccuracies in basic statistical inference based on such fuzzy data. In particular, we focus on inference on population mean and variance of single population as well as two population one-sample and also address the proportion problem in the pairedtest framework. In the testing of hypothesis framework, both the size and power of the tests are looked at. The results are mixed, as we observe that fuzziness of data impacts the inference substantially in some problems, while it has virtually no impact in some other problem domain.